Calculate the product below and give your answer in scientific notation. $ {\left(7.8\times 10^{3} \right) \times \left(1.0\times 10^{4} \right) =\ ?} $
Solution: Start by collecting the significands and exponents. $ ({7.8} \times {10^{3}}) \times ({1.0} \times {10^{4}}) = ({7.8} \times {1.0}) \times ({10^{3}} \times {10^{4}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {7.8} \times {10^{3 \,+\, 4}}$ $= {7.8} \times {10^{7}}$